📑 Topics on this page (Jump to Topic):
📌 1. Percentage-Fraction Table
Percent means "per hundred". x% = x/100. x% of a quantity = quantity × x/100.
| Fraction | % | Fraction | % |
|---|---|---|---|
| 1/2 | 50% | 1/9 | 11.11% |
| 1/3 | 33.33% | 1/11 | 9.09% |
| 1/4 | 25% | 1/12 | 8.33% |
| 1/5 | 20% | 1/16 | 6.25% |
| 1/6 | 16.67% | 1/20 | 5% |
| 1/7 | 14.28% | 1/25 | 4% |
| 1/8 | 12.5% | 3/8 | 37.5% |
💡 Shortcut Trick: Memorise the table — values like 37.5% = 3/8, 62.5% = 5/8, 87.5% = 7/8 save time.
📌 2. Increase, Decrease & Successive Change
📘 Formulas:
- % change = (change / original value) × 100
- Successive changes a% and b%: net = a + b + ab/100 (take decrease as negative)
- If A is r% more than B, then B is [r/(100 + r)] × 100 % less than A
- If A is r% less than B, then B is [r/(100 − r)] × 100 % more than A
- If price rises r%, cut in consumption to keep expenditure same = [r/(100 + r)] × 100 %
- Population after n years = P(1 + r/100)n; n years ago = P/(1 + r/100)n
⚠️ Exam Traps:
- A 10% rise followed by a 10% fall = net 1% decrease (not zero).
- "A is 25% more than B" ≠ "B is 25% less than A" (it is 20%).
📌 3. Elections, Exams & Income-Expenditure
- Election: two candidates; winner gets x% → winning margin = (2x − 100)% of valid votes.
- Exam: pass marks = maximum × pass %. If a% fails by x and b% passes by y → maximum = (x + y)/(b − a) × 100.
- Income-expenditure: savings = income − expenditure; when both change, compute the new savings separately.
✏️ Example: 35% of a number = 140 → number = 140 × 100/35 = 400.
📌 4. Practice MCQs
📝 Practice MCQs (prepared by SF Prep — not PYQs)
Q1. 55% of a number is 165. What is the number? Practice
Correct answer: (B)
Solution: Number = 165 × 100/55 = 300.
Solution: Number = 165 × 100/55 = 300.
Q2. The price of an item first has a 40% increase and then a 30% decrease. What is the net effect? Practice
Correct answer: (C)
Solution: a + b + ab/100 = 40 + (-30) + (40×-30)/100 = -2% → 2% decrease.
Solution: a + b + ab/100 = 40 + (-30) + (40×-30)/100 = -2% → 2% decrease.
Q3. The price of sugar rises by 60%. By what percent must consumption be reduced to keep expenditure unchanged? Practice
Correct answer: (D)
Solution: Reduction = [r/(100 + r)] × 100 = [60/160] × 100 = 37.5%.
Solution: Reduction = [r/(100 + r)] × 100 = [60/160] × 100 = 37.5%.
Q4. The population of a town is 10000 and grows at 5% per annum. Population after 2 years will be: Practice
Correct answer: (A)
Solution: P(1 + r/100)n = 10000 × (105/100)2 = 11025.
Solution: P(1 + r/100)n = 10000 × (105/100)2 = 11025.
Q5. In an election between two candidates, the winner got 65% of valid votes and won by 6000 votes. Total valid votes were: Practice
Correct answer: (B)
Solution: Margin = 65% − 35% = 30% = 6000 → total = 6000 × 100/30 = 20000.
Solution: Margin = 65% − 35% = 30% = 6000 → total = 6000 × 100/30 = 20000.
Q6. In an exam, a student scoring 32% fails by 10 marks and another scoring 40% gets 14 marks more than the pass mark. Find the maximum marks. Practice
Correct answer: (C)
Solution: (40 − 32)% = 10 + 14 = 24 → maximum = 24 × 100/8 = 300. (Pass mark = 106)
Solution: (40 − 32)% = 10 + 14 = 24 → maximum = 24 × 100/8 = 300. (Pass mark = 106)
Q7. The price of an article changes from ₹250 to ₹300. The percentage change is: Practice
Correct answer: (D)
Solution: Change/original × 100 = 50/250 × 100 = 20% increase.
Solution: Change/original × 100 = 50/250 × 100 = 20% increase.
Q8. In a class, 60% are boys. 20% of the boys and 40% of the girls passed. The overall pass percentage is: Practice
Correct answer: (A)
Solution: Take 100 students: 12 of 60 boys and 16 of 40 girls pass → 28%.
Solution: Take 100 students: 12 of 60 boys and 16 of 40 girls pass → 28%.
Q9. What is 62.5% of 640? Practice
Correct answer: (B)
Solution: 640 × 62.5/100 = 400.
Solution: 640 × 62.5/100 = 400.
Q10. 72% of a number is 288. What is the number? Practice
Correct answer: (C)
Solution: Number = 288 × 100/72 = 400.
Solution: Number = 288 × 100/72 = 400.
Q11. The price of an item first has a 30% increase and then a 10% increase. What is the net effect? Practice
Correct answer: (D)
Solution: a + b + ab/100 = 30 + (10) + (30×10)/100 = 43% → 43% increase.
Solution: a + b + ab/100 = 30 + (10) + (30×10)/100 = 43% → 43% increase.
Q12. The price of sugar rises by 25%. By what percent must consumption be reduced to keep expenditure unchanged? Practice
Correct answer: (A)
Solution: Reduction = [r/(100 + r)] × 100 = [25/125] × 100 = 20%.
Solution: Reduction = [r/(100 + r)] × 100 = [25/125] × 100 = 20%.
Q13. The population of a town is 64000 and grows at 5% per annum. Population after 2 years will be: Practice
Correct answer: (B)
Solution: P(1 + r/100)n = 64000 × (105/100)2 = 70560.
Solution: P(1 + r/100)n = 64000 × (105/100)2 = 70560.
Q14. In an election between two candidates, the winner got 52% of valid votes and won by 2400 votes. Total valid votes were: Practice
Correct answer: (C)
Solution: Margin = 52% − 48% = 4% = 2400 → total = 2400 × 100/4 = 60000.
Solution: Margin = 52% − 48% = 4% = 2400 → total = 2400 × 100/4 = 60000.
Q15. In an exam, a student scoring 40% fails by 25 marks and another scoring 48% gets 17 marks more than the pass mark. Find the maximum marks. Practice
Correct answer: (D)
Solution: (48 − 40)% = 25 + 17 = 42 → maximum = 42 × 100/8 = 525. (Pass mark = 235)
Solution: (48 − 40)% = 25 + 17 = 42 → maximum = 42 × 100/8 = 525. (Pass mark = 235)
Q16. In a class, 60% are boys. 20% of the boys and 30% of the girls passed. The overall pass percentage is: Practice
Correct answer: (A)
Solution: Take 100 students: 12 of 60 boys and 12 of 40 girls pass → 24%.
Solution: Take 100 students: 12 of 60 boys and 12 of 40 girls pass → 24%.
Q17. What is 62.5% of 360? Practice
Correct answer: (B)
Solution: 360 × 62.5/100 = 225.
Solution: 360 × 62.5/100 = 225.
Q18. 72% of a number is 360. What is the number? Practice
Correct answer: (C)
Solution: Number = 360 × 100/72 = 500.
Solution: Number = 360 × 100/72 = 500.
Q19. The price of an item first has a 25% increase and then a 25% decrease. What is the net effect? Practice
Correct answer: (D)
Solution: a + b + ab/100 = 25 + (-25) + (25×-25)/100 = -6.25% → 6.25% decrease.
Solution: a + b + ab/100 = 25 + (-25) + (25×-25)/100 = -6.25% → 6.25% decrease.
Q20. If A's income is 20% more than B's, by what percent is B's income less than A's? Practice
Correct answer: (A)
Solution: [20/(100 + 20)] × 100 = 16.67%.
Solution: [20/(100 + 20)] × 100 = 16.67%.